Problem: Simplify the expression. $(3t^{4}-7t^{2}+6t)(2t^{4}-7t^{3})$
Solution: First use the distributive property. $ 3 t^4 (2 t^4) + 3 t^4 (-7 t^3) - 7 t^2 (2 t^4) - 7 t^2 (-7 t^3) + 6 t (2 t^4) + 6 t (-7 t^3) $ Simplify. $ 6t^{8} - 21t^{7} - 14t^{6} + 49t^{5} + 12t^{5} - 42t^{4} $ $6t^{8}-21t^{7}-14t^{6}+61t^{5}-42t^{4}$ Identify like terms. $ { 6t^{8}} {- 21t^{7}} {- 14t^{6}} {+ 49t^{5}} {+ 12t^{5}} {- 42t^{4}} $ Add the coefficients. $ { 6t^{8}} { -21t^{7}} { -14t^{6}} {+ 61t^{5}} { -42t^{4}} $